Assignment $5$: Problem $6$

$(1$ point$)$

The system of first order differential equations:

$y_1^{\text{'}}=-13y_1+2y_2,y_1(0)=5$

$y_2^{\text{'}}=-52y_1+7y_2,y_2(0)=23$

has solution:

$y_1(t)=$

$y_2(t)=$

Note: You must express the answer in terms of real numbers only.